English
Related papers

Related papers: Coupling Graph Neural Networks with Fractional Ord…

200 papers

Modern graph representation learning works mostly under the assumption of dealing with regularly sampled temporal graph snapshots, which is far from realistic, e.g., social networks and physical systems are characterized by continuous…

Machine Learning · Computer Science 2024-09-11 Alessio Gravina , Daniele Zambon , Davide Bacciu , Cesare Alippi

In this paper we propose the use of continuous residual modules for graph kernels in Graph Neural Networks. We show how both discrete and continuous residual layers allow for more robust training, being that continuous residual layers are…

Machine Learning · Computer Science 2019-11-27 Pedro H. C. Avelar , Anderson R. Tavares , Marco Gori , Luis C. Lamb

Graph Neural Networks (GNNs) and differential equations (DEs) are two rapidly advancing areas of research that have shown remarkable synergy in recent years. GNNs have emerged as powerful tools for learning on graph-structured data, while…

Machine Learning · Computer Science 2025-06-30 Zewen Liu , Xiaoda Wang , Bohan Wang , Zijie Huang , Carl Yang , Wei Jin

Neural ordinary differential equations (neural ODEs) can effectively learn dynamical systems from time series data, but their behavior on graph-structured data remains poorly understood, especially when applied to graphs with different size…

Physics and Society · Physics 2026-02-10 Moritz Laber , Tina Eliassi-Rad , Brennan Klein

Graph neural Ordinary Differential Equations (ODE) combine neural ODE with the message passing mechanism of Graph Neural Networks (GNN), providing a continuous-time modeling method for graph representation learning. However, in dynamic…

Machine Learning · Computer Science 2026-04-29 Xiaoyi Wang , Zhiqiang Wang , Jianqing Liang , Xingwang Zhao , Chuangyin Dang , Zhen Jin , Jiye Liang

Many works show that node-level predictions of Graph Neural Networks (GNNs) are unrobust to small, often termed adversarial, changes to the graph structure. However, because manual inspection of a graph is difficult, it is unclear if the…

Machine Learning · Computer Science 2023-05-03 Lukas Gosch , Daniel Sturm , Simon Geisler , Stephan Günnemann

Continuous-depth graph neural networks, also known as Graph Neural Differential Equations (GNDEs), combine the structural inductive bias of Graph Neural Networks (GNNs) with the continuous-depth architecture of Neural ODEs, offering a…

Machine Learning · Computer Science 2026-04-21 Mingsong Yan , Charles Kulick , Sui Tang

Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying…

Numerical Analysis · Mathematics 2025-06-18 Matteo Caldana , Jan S. Hesthaven

We present a novel model Graph Neural Stochastic Differential Equations (Graph Neural SDEs). This technique enhances the Graph Neural Ordinary Differential Equations (Graph Neural ODEs) by embedding randomness into data representation using…

Machine Learning · Computer Science 2023-08-25 Richard Bergna , Felix Opolka , Pietro Liò , Jose Miguel Hernandez-Lobato

This paper proposes fractional order graph neural networks (FGNNs), optimized by the approximation strategy to address the challenges of local optimum of classic and fractional graph neural networks which are specialised at aggregating…

Machine Learning · Computer Science 2021-07-07 Zijian Liu , Chunbo Luo , Shuai Li , Peng Ren , Geyong Min

There has been an increasing interest in inferring future links on temporal knowledge graphs (KG). While links on temporal KGs vary continuously over time, the existing approaches model the temporal KGs in discrete state spaces. To this…

Machine Learning · Computer Science 2022-06-03 Zhen Han , Zifeng Ding , Yunpu Ma , Yujia Gu , Volker Tresp

Recent studies show that Graph Neural Networks (GNNs) are vulnerable to adversarial attack, i.e., an imperceptible structure perturbation can fool GNNs to make wrong predictions. Some researches explore specific properties of clean graphs…

Machine Learning · Computer Science 2022-03-23 Guangqian Yang , Yibing Zhan , Jinlong Li , Baosheng Yu , Liu Liu , Fengxiang He

Graph neural networks (GNNs) are an emerging model for learning graph embeddings and making predictions on graph structured data. However, robustness of graph neural networks is not yet well-understood. In this work, we focus on node…

Machine Learning · Computer Science 2019-12-24 James Fox , Sivasankaran Rajamanickam

Graph Neural Networks (GNNs) have established themselves as a key component in addressing diverse graph-based tasks. Despite their notable successes, GNNs remain susceptible to input perturbations in the form of adversarial attacks. This…

Machine Learning · Computer Science 2024-09-13 Moshe Eliasof , Davide Murari , Ferdia Sherry , Carola-Bibiane Schönlieb

Continuous graph neural networks (CGNNs) have garnered significant attention due to their ability to generalize existing discrete graph neural networks (GNNs) by introducing continuous dynamics. They typically draw inspiration from…

Neural and Evolutionary Computing · Computer Science 2025-07-15 Nan Yin , Mengzhu Wan , Li Shen , Hitesh Laxmichand Patel , Baopu Li , Bin Gu , Huan Xiong

Graph Neural Networks (GNNs) have become the standard for graph representation learning but remain vulnerable to structural perturbations. We propose a novel framework that integrates persistent homology features with stability…

Machine Learning · Computer Science 2025-12-17 Jelena Losic

This paper presents a new look at the neural network (NN) robustness problem, from the point of view of graph theory analysis, specifically graph curvature. Graph curvature (e.g., Ricci curvature) has been used to analyze system dynamics…

Machine Learning · Computer Science 2024-12-17 Shuhang Tan , Jayson Sia , Paul Bogdan , Radoslav Ivanov

Neural ODEs (NODEs) have emerged as powerful tools for modeling time series data, offering the flexibility to adapt to varying input scales and capture complex dynamics. However, they face significant challenges: first, their reliance on…

Machine Learning · Computer Science 2025-10-07 Muhao Guo , Yang Weng

Neural Ordinary Differential Equations (ODE) are a promising approach to learn dynamic models from time-series data in science and engineering applications. This work aims at learning Neural ODE for stiff systems, which are usually raised…

Numerical Analysis · Mathematics 2021-10-04 Suyong Kim , Weiqi Ji , Sili Deng , Yingbo Ma , Christopher Rackauckas

Spatial-temporal forecasting has attracted tremendous attention in a wide range of applications, and traffic flow prediction is a canonical and typical example. The complex and long-range spatial-temporal correlations of traffic flow bring…

Machine Learning · Computer Science 2021-06-25 Zheng Fang , Qingqing Long , Guojie Song , Kunqing Xie